Pulsed Control of Thermoacoustic Instabilities: Analysis and Experiment

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
J. Matthew Carson ◽  
William T. Baumann ◽  
William R. Saunders
Keyword(s):  
Phase Shift ◽  
Limit Cycle ◽  
Fourier Component ◽  
Linear Phase ◽  
Cycle Frequency ◽  
Thermoacoustic Instabilities ◽  
Control Authority ◽  
Subharmonic Frequency ◽  
Cycling Behavior ◽  
Instability Frequency

Thermoacoustic instabilities in combustors have been suppressed using phase-shift algorithms pulsing an on-off actuator at the limit cycle frequency (flc) or at the subharmonics of flc. It has been suggested that control at a subharmonic rate may extend the actuator lifetime and possibly require less actuator bandwidth. This paper examines the mechanism of subharmonic control in order to clarify the principles of operation and subsequently identify potential advantages for combustion control. Theoretical and experimental arguments show that there must be a Fourier component of the subharmonic control signal at flc in order to stabilize the limit cycling behavior. It is also demonstrated that the magnitude of that Fourier component must be equivalent to the signal magnitude for a linear phase-shift controller that operates directly at flc. The concept of variable-subharmonic control is introduced whereby the actuator is pulsed at the instability frequency to initially stabilize the system and then is pulsed at a subharmonic frequency to maintain stability. These results imply that an actuator used for subharmonic control cannot be effective unless its bandwidth spans the instability frequency. The advantage of reduced cycling may still be realized but will require higher control authority to produce the same effect as an actuator pulsed at the instability frequency.

Control of Combustor Instabilities Using an Artificial Neural Network

2000 ◽  
Author(s):  
Michael A. Vaudrey ◽  
William R. Saunders
Keyword(s):  
Neural Network ◽  
Frequency Response ◽  
Limit Cycle ◽  
Design Process ◽  
Open Loop ◽  
Operating Conditions ◽  
Feedback Controller ◽  
Phase Shifting ◽  
Cycle Frequency ◽  
Thermoacoustic Instabilities

It is well-known that phase-shifting controllers used for active combustion control must be manually adjusted in order to maintain control over a broad range of operating combustor operating conditions. If one assumes that the thermoacoustic instabilities are linearly stabilizable, then what is needed is a method to determine, and ultimately predict, the frequency response of the plant for any range of operating conditions, so the controller design can be automatically updated to track the changing plant gain/phase relationships that are observed with changing heat release. A unique test-based, design process has been proposed to predict the gain/phase characteristics required of a proportional, phase-shifting controller that can stabilize the thermoacoustic instabilities. In this paper, that process is used to automate the design of a fixed-gain feedback controller that limits the amplitudes of any feedback induced instabilities (to some pre-specified level) while providing the best control of the targeted limit cycling pressure oscillations. The paper describes how a neural network was trained, using the suggested design process, to predict the frequency response of the thermoacoustics in a tube combustor at frequencies adjacent to the limit cycle frequency using certain operating conditions that included a sparsely-sampled temperature profile, total air/fuel flow rate, and equivalence ratio. The neural net training was performed using complex valued, open-loop frequency response function data as the desired signal with the previously mentioned operating conditions as the input signals. (The open loop data was collected for a narrow frequency range surrounding the limit cycle instability by performing a sine dwell at discrete frequencies). Once the neural network was trained, it was used to predict the approximate phase and gain margins as a function of temperature and flow conditions. The margins were then used to automatically update and design a fixed shape feedback controller having the proper phase and magnitude to ensure stability and control in the face of changing operating conditions. A companion paper describes the methodology that underlies the automated design of the feedback controller gain and phase delay.

A Test-Based Methodology for A Priori Selection of Gain/Phase Relationships in Proportional, Phase-Shifting Control of Combustion Instabilities

2000 ◽  
Author(s):  
Michael A. Vaudrey ◽  
William R. Saunders ◽  
Bryan Eisenhower
Keyword(s):  
Feedback Control ◽  
Frequency Response ◽  
Limit Cycle ◽  
Design Method ◽  
Phase Relationship ◽  
Operating Conditions ◽  
Phase Shifting ◽  
Nonlinear Phenomena ◽  
The Absolute ◽  
Instability Frequency

Feedback control system design, for general single-in-single-out (SISO) applications, requires accurate knowledge of the loop transfer function. Active combustion control design is usually implemented using such SISO architectures, but is quite challenging because the thermoacoustic response results from a relatively unknown, self-excited system and nonlinear processes that must be understood before learning the gain/phase relationship of the system precisely at the instability frequency. However, recent experiments have shown that it is possible to obtain accurate measurements of the relevant loop transfer (frequency response) functions at frequencies adjacent to the instability frequency. Using a simple tube combustor, operating with a premixed, gaseous, burner-stabilized flame, the loop frequency response measurements have been used to develop a methodology that leads to ‘test-based predictions’ of the absolute phase settings and ‘best’ gain settings for a proportional, phase-shifting controller commanding an acoustic actuator in the combustor. The contributions of this methodology are twofold. First, it means that a manual search for the required phase setting of the controller is no longer necessary. In fact, this technique allows the absolute value of controller phase to be determined without running the controller. To the authors’ knowledge, this has not been previously reported in the literature. In addition, the ‘best’ gain setting of the controller, based on this new design approach, can be defined as one that eliminates or reduces the limit cycle amplitude as much as possible within the constraint of avoiding generation of any controller-induced instabilities. (This refers to the generation of ‘new’ peaks in the controlled acoustic pressure spectrum.) It is shown that this tradeoff in limit cycle suppression and avoidance of controller-induced instabilities is a manifestation of the well-known tradeoff in the sensitivity/complementary sensitivity function for feedback control solutions. The focus of this article is limited to the presentation of the design method and does not discuss the detailed nonlinear phenomena that must be understood to determine the optimal gain/phase settings at the limit cycle frequency for a real (versus theoretical) combustor system. A companion paper describes how the proposed design method can be used to generate an AI controller that maintains stabilizing control for a range of changing operating conditions.

Nonlinear Heat-Release/Acoustic Model for Thermoacoustic Instability in Lean Premixed Combustors

1999 ◽  
Vol 121 (3) ◽  
pp. 415-421 ◽  
Author(s):  
A. A. Peracchio ◽  
W. M. Proscia
Keyword(s):  
Heat Release ◽  
Limit Cycle ◽  
Gas Turbines ◽  
Pressure Fluctuations ◽  
Parametric Model ◽  
Operating Conditions ◽  
Cycle Frequency ◽  
Thermoacoustic Instability ◽  
Lean Premixed ◽  
Industrial Gas Turbines

Lean premixed combustors, such as those used in industrial gas turbines to achieve low emissions, are often susceptible to the thermoacoustic combustion instabilities, which manifest themselves as pressure and heat release oscillations in the combustor. These oscillations can result in increased noise and decreased durability due to vibration and flame motion. A physically based nonlinear parametric model has been developed that captures this instability. It describes the coupling of combustor acoustics with the rate of heat release. The model represents this coupling by accounting for the effect of acoustic pressure fluctuations on the varying fuel/air ratio being delivered to the flame, causing a fluctuating heat release due to both fuel air ratio variations and flame front oscillations. If the phasing of the fluctuating heat release and pressure are proper, an instability results that grows into a limit cycle. The nonlinear nature of the model predicts the onset of the instability and additionally captures the resulting limit cycle. Tests of a lean premixed nozzle run at engine scale and engine operating conditions in the UTRC single nozzle rig, conducted under DARPA contract, exhibited instabilities. Parameters from the model were adjusted so that analytical results were consistent with relevant experimental data from this test. The parametric model captures the limit cycle behavior over a range of mean fuel air ratios, showing the instability amplitude (pressure and heat release) to increase and limit cycle frequency to decrease as mean fuel air ratio is reduced.

scholarly journals New Phase Shifting Algorithms Insensitive to Linear Phase Shift Errors

10.14311/376 ◽  
2002 ◽  
Vol 42 (4) ◽  
Author(s):  
J. Novák
Keyword(s):  
Phase Shift ◽  
Evaluation Process ◽  
Phase Shifting ◽  
Linear Phase ◽  
Phase Errors ◽  
Arbitrary Phase ◽  
Phase Calculation ◽  
Calculation Algorithms ◽  
Phase Evaluation ◽  
New Phase

This article describes and analyses multistep algorithms for evaluating of the wave field phase in interferometric measurements using the phase shifting technique. New phase shifting algorithms are proposed, with a constant but arbitrary phase shift between captured frames of the intensity of the interference field. The phase evaluation process then does not depend on linear phase shift errors. A big advantage of the described algorithms is their ability to determine the phase shift value at every point of the detector plane. A detailed analysis of these algorithms with respect to main factors that affect interferometric measurements is then carried out. The dependency of these algorithms on phase shift values is also studied several phase calculation algorithms are proposed. These are compared with respect to the resulting phase errors.

A self-consistent formulation for the sensitivity analysis of finite-amplitude vortex shedding in the cylinder wake

2016 ◽  
Vol 800 ◽  
pp. 327-357 ◽  
Author(s):  
P. Meliga ◽  
E. Boujo ◽  
F. Gallaire
Keyword(s):  
Sensitivity Analysis ◽  
Limit Cycle ◽  
Stokes Equations ◽  
Finite Amplitude ◽  
Cylinder Wake ◽  
Mean Flow ◽  
Cycle Frequency ◽  
Flow Perturbation ◽  
Self Consistent ◽  
The Mean

We use the adjoint method to compute sensitivity maps for the limit-cycle frequency and amplitude of the Bénard–von Kármán vortex street in the wake of a circular cylinder. The sensitivity analysis is performed in the frame of the semi-linear self-consistent model recently introduced by Mantič et al. (Phys. Rev. Lett., vol. 113, 2014, 084501), which allows us to describe accurately the effect of the control on the mean flow, but also on the finite-amplitude fluctuation that couples back nonlinearly onto the mean flow via the formation of Reynolds stress. The sensitivity is computed with respect to arbitrary steady and synchronous time-harmonic body forces. For a small amplitude of the control, the theoretical variations of the limit-cycle frequency predict well those of the controlled flow, as obtained from either self-consistent modelling or direct numerical simulation of the Navier–Stokes equations. This is not the case if the variations are computed in the simpler mean flow approach overlooking the coupling between the mean and fluctuating components of the flow perturbation induced by the control. The variations of the limit-cycle amplitude (that falls out the scope of the mean flow approach) are also correctly predicted, meaning that the approach can serve as a relevant and systematic guideline to control strongly unstable flows exhibiting non-small, finite amplitudes of oscillation. As an illustration, we apply the method to control by means of a small secondary control cylinder and discuss the obtained results in the light of the seminal experiments of Strykowski & Sreenivasan (J. Fluid Mech., vol. 218, 1990, pp. 71–107).

Study of the parameters of a difference image in the presence of a linear phase shift

Laser Physics ◽  
2006 ◽  
Vol 16 (3) ◽  
pp. 488-494
Author(s):  
S. N. Malov ◽  
A. A. Smirnov
Keyword(s):  
Phase Shift ◽  
Linear Phase ◽  
Difference Image
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